Whether focused on vegetation patterns [1]}, schooling and swarming [2]}, [3]}, collective cell dynamics [4]}, [5]}, [6]}, [7]}, [8]}, or another complex system, researchers use a wide range of mathematical models to study pattern formation. These approaches include stochastic individual-based models, which may operate on or off lattice, and macroscopic models in the form of partial differential equations. This wealth of frameworks is a benefit, since different types of models have complementary strengths and weaknesses, but it also presents challenges. Relating different models of the same biological system is not straightforward, particularly when considering spatial dynamics and detailed, stochastic models, which often rely on qualitative observation to judge model output. Motivated by this challenge, we show how to adapt methods from topological data analysis and computational geometry to quantitatively describe two models of the same biological system in a comparable way. For concreteness, we center our study on zebrafish-skin patterns, and we apply our methods to two stochastic, individual-based models [9]}, [10]}.
